Download Reteach 6-1 to 6-3

NAME
DATE
PERIOD
Lesson 1 Reteach
Powers and Exponents
A product of like factors can be written using a base, the number used as a factor, and an exponent,
which tells how many times the base is used as a factor. Numbers expressed using exponents are
called powers. For example, 100 and 1,000 are powers of 10 because they can be written as
10^ and 10^
Example 1
Write 4 x 4 x 4 x 4 x 4 u s i n g a n exponent.
4 x 4 x 4 x 4 x 4
= 4^
4 is used
as a factor five times.
Example 2
Write 3'* as a p r o d u c t of the same factor. T h e n find the v a l u e .
The base is 3. T h e exponent is 4. So, 3 is used as a factor four times.
= 3 x 3 x 3 x 3
Write
= 81
Multiply.
3^
as a product.
Exercises
Write e a c h p r o d u c t u s i n g a n exponent.
1. 4 x 4 x 4
2. 7 x 7 x 7 x 7 x 7
3. 9 x 9 x 9 x 9
4. 8 x 8 x 8 x 8 x 8 x 8
5. 1 x 1 x 1 x 1
6.
2 x 2 x 2 x 2 x 2 x 2 x 2
Write e a c h p o w e r a s a p r o d u c t of t h e same factor. T h e n find the v a l u e .
7. 5 '
9. 2«
1 1 . 1.1"
8. 6^
10. 3«
12. 0.7=*
13. MAMMALS There are about 10^ species of bats i n the world. Write 10^ as a product of
the same factor. Then find the value.
14. LANDSCAPE T h e deepest point of the Grand Canyon i n Arizona is a little over 18^ feet
deep. How deep is the canyon at this point?
Course 1 • Chapter 6 Expressions
87
PERIOD
DATE
NAME
Lesson 2 Reteach
Numerical Expressions
Order of Operations
1. Simplify the expressions inside grouping symbols, like parentheses.
2. Find the value of all powers.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Example 1
F i n d t h e value of 48 ^ (3 + 3) - 2\
48 ^ (3 + 3) - 2^ =
=
=
=
48
6 - 2^
48
6 - 4
8 - 4
4
Simplify the expression inside the parentheses.
Find 2'.
Divide 48 by 6.
Subtract 4 from 8.
Example 2
Write a n d solve a n expression to find the total cost of p l a n t i n g
flowers i n the garden.
Item
Cost per Item
N u m b e r of Items Needed
Pack of flowers
$4
5
B a g of dirt
$3
1
Bottle of fertilizer
$4
1
cost of 5 flower packs
Words
5
Expression
X
plus
cost of dirt
plus
cost of fertilizer
+
$3
+
$4
$4
5 X $4 + $3 + $4 = $20 + $3 + $4
= $23 + $4
= $27
Multiply 5 by $4.
Add $20 and $3.
Add $23 and $4.
The total cost of planting flowers i n the garden i s $27.
Exercises
F i n d t h e v a l u e of e a c h expression.
1. 7 + 2
X
3
2. 12
4. 8 x 8 - r 4
7. 25 ^ 5 + 6
X
(12 - 4)
-r
3 + 5
3. 16 - (4 + 5)
5. 1 0 + 1 4 H - 2
6. 3 x 3 +
2 x 4
8. 80 - 8 x 3^
9. 11 x (9 - 2^)
10. GARDENING Refer to Example 2 above. Suppose that the gardener did not buy enough
flowers and goes back to the store to purchase four more packs. She also purchases a
shovel for $16. Write a n expression that shows the total amount she spent to plant
flowers i n her garden.
Course 1 • Chapter 6 Expressions
89
NAME
DATE
PERIOD
Lesson 3 Reteach
Algebra: Variables and Expressions
• A variable is a symbol, usually a letter, used to represent a number.
• In addition to the symbol x , the other ways to show multiplication are 2-3, 5t, and st.
• Algebraic expressions contain at least one variable and at least one operation.
Example 1
E v a l u a t e 35 + x i f jc = 6.
35 + a: = 35 + 6
= 41
Replace x with 6.
Add 35 and 6.
Example 2
E v a l u a t e y + xifx
= 21 a n d y = 35.
y + x = 35 + 21
= 56
Replace x with 21 and y with 35.
Add 35 and 21.
Example 3
E v a l u a t e 4n + 3 i f n = 2.
4n+ 3 = 4- 2 + 3
= 8+3
= 11
Replace n with 2.
Find the product of 4 and 2.
Add 8 and 3.
Example 4
E v a l u a t e 4n — 2 i f n = 5.
4n- 2= 4 . 5 - 2
= 20-2
= 18
Replace n with 5.
Find the product of 4 and 5.
Subtract 2 from 20.
Exercises
E v a l u a t e e a c h expression i f y = 4.
1.3+3/
2. >- + 8
3. 4 - 3 /
4. 9y
5. 15y
6. 3003-
7. y'
8.
+ 18
9. 3^^ + 3 . 7
E v a l u a t e e a c h expression i f m = 3 a n d k = 10.
10. 16 + m
1 1 . 4k
12. m • ^
13. m + k
14. 7m + k
15. 6^ + m
16. 3^ - 4m
17. 2mk
18. 5k - 6m
19. 20m + k
20.
Course 1 • Chapter 6 Expressions
m3 +
2k''
21. A:^ + (2 + m)
91